Subgroups — C₃₁×#62541 #21519300

Order 7936.

2026 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3373	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3332	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3306	C₂	1	8	yes	maximal, complemented
6	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3227	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3184	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3141	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×2₋¹⁺⁴	—	2	1	no	—
16	C₃₁×#559	—	2	1	no	—
17	C₃₁×#559	C₂²	1	2	yes	—
18	C₃₁×#550	—	2	1	no	—
19	C₃₁×#550	C₂²	1	2	yes	—
20	D₄×Q₈×C₃₁	—	2	1	no	—
21	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
22	C₃₁×#547	—	2	2	no	—
23	C₃₁×#547	—	2	1	no	—
24	C₃₁×#547	C₂²	1	4	yes	—
25	C₃₁×#547	C₂²	1	2	yes	complemented
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#546	C₂²	1	4	yes	—
28	C₃₁×#540	—	2	2	no	—
29	C₃₁×#536	—	2	1	no	—
30	C₃₁×#536	—	2	2	no	—
31	C₃₁×#535	—	2	1	no	—
32	C₃₁×#533	C₂²	1	1	yes	characteristic
33	C₃₁×#532	C₂²	1	2	yes	—
34	C₃₁×#532	C₂²	1	1	yes	characteristic
35	C₃₁×#532	C₂²	1	2	yes	—
36	C₃₁×#532	C₂²	1	2	yes	complemented
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
40	C₃₁×#518	—	2	1	no	—
41	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#498	C₂²	1	2	yes	complemented
44	C₃₁×#493	C₂²	1	2	yes	—
45	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#489	C₂²	1	8	yes	complemented
47	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#487	C₂²	1	2	yes	complemented
49	C₃₁×#486	C₂²	1	4	yes	—
50	C₃₁×#486	C₂²	1	2	yes	—
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#486	C₂²	1	2	yes	—
53	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#483	C₂²	1	4	yes	—
55	C₃₁×#481	C₂²	1	8	yes	complemented
56	C₃₁×#476	C₂²	1	8	yes	complemented
57	C₃₁×#475	C₂²	1	4	yes	complemented
58	C₃₁×#469	C₂²	1	8	yes	complemented
59	C₃₁×#465	C₂²	1	4	yes	—
60	C₃₁×#463	C₂²	1	8	yes	complemented
61	C₃₁×#459	C₂²	1	4	yes	—
62	C₃₁×#449	C₂²	1	8	yes	complemented
63	C₃₁×#447	C₂²	1	4	yes	—
64	C₃₁×#446	C₂²	1	2	yes	complemented
65	C₃₁×#442	C₂²	1	8	yes	complemented
66	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#436	C₂²	1	2	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	—
69	C₃₁×#431	C₂²	1	1	yes	characteristic
70	C₃₁×#431	C₂²	1	2	yes	complemented
71	C₃₁×#417	C₂²	1	8	yes	complemented
72	C₂×C₃₁×#102	C₂²	1	4	yes	—
73	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
74	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
75	C₃₁×2₋¹⁺⁴	—	4	8	no	—
76	C₂×#41×C₃₁	—	2	4	no	—
77	C₂×#41×C₃₁	—	2	2	no	—
78	C₂×#41×C₃₁	—	2	1	no	—
79	C₂×#41×C₃₁	—	2	2	no	—
80	C₂×#41×C₃₁	—	2	2	no	—
81	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
82	C₂×#41×C₃₁	C₂³	1	4	yes	—
83	C₂²×Q₈×C₃₁	—	2	2	no	—
84	C₂²×Q₈×C₃₁	—	2	1	no	—
85	C₂²×Q₈×C₃₁	—	2	2	no	—
86	C₂²×D₄×C₃₁	—	2	1	no	—
87	C₂²×D₄×C₃₁	—	2	1	no	—
88	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
89	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
90	C₂×D₈×C₃₁	C₂³	1	8	yes	—
91	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
93	C₃₁×C₄⋊Q₈	—	2	1	no	—
94	C₃₁×C₄⋊Q₈	—	2	1	no	—
95	C₃₁×C₄⋊Q₈	—	2	2	no	—
96	C₃₁×C₄⋊Q₈	—	2	2	no	—
97	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×#127	—	2	2	no	—
104	C₃₁×#127	—	2	1	no	—
105	C₃₁×#127	—	2	1	no	—
106	C₃₁×#127	C₂³	1	2	yes	—
107	C₃₁×#127	C₂³	1	2	yes	—
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#125	—	2	1	no	—
110	C₃₁×#124	—	2	2	no	—
111	C₃₁×#124	—	2	1	no	—
112	C₃₁×#124	—	2	2	no	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	C₂³	1	4	yes	—
115	C₃₁×#123	—	2	4	no	—
116	C₃₁×#123	—	2	4	no	—
117	C₃₁×#123	—	2	4	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×C₂²⋊Q₈	—	2	1	no	—
121	C₃₁×C₂²⋊Q₈	—	2	2	no	—
122	C₃₁×C₂²⋊Q₈	—	2	4	no	—
123	C₃₁×C₂²⋊Q₈	—	2	4	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	2	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	1	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	C₂³	1	2	yes	—
134	C₃₁×#121	C₂³	1	4	yes	—
135	C₃₁×#121	C₂³	1	4	yes	—
136	C₃₁×#120	—	2	4	no	—
137	C₄×Q₈×C₃₁	—	2	1	no	—
138	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
139	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₄×D₄×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	2	no	—
143	C₄×D₄×C₃₁	—	2	2	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	1	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	D₄	1	2	yes	—
149	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₄×D₄×C₃₁	C₂³	1	4	yes	—
153	C₄×D₄×C₃₁	C₂³	1	2	yes	—
154	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₃₁×#117	—	2	1	no	—
156	C₃₁×#117	D₄	1	1	yes	characteristic
157	C₃₁×#117	D₄	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
159	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
165	C₃₁×#106	C₂³	1	4	yes	—
166	C₃₁×#106	C₂³	1	8	yes	—
167	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
169	C₃₁×#103	C₂³	1	4	yes	—
170	C₃₁×#103	C₂³	1	8	yes	—
171	C₃₁×#102	C₂³	1	8	yes	—
172	C₃₁×#102	C₂³	1	8	yes	—
173	C₃₁×#102	C₂³	1	8	yes	—
174	C₃₁×#102	C₂³	1	4	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₃₁	C₂³	1	2	yes	—
181	C₄×C₈×C₃₁	C₂³	1	2	yes	—
182	C₂⁴×C₃₁	—	2	2	no	—
183	#41×C₃₁	—	2	4	no	—
184	#41×C₃₁	—	4	8	no	—
185	#41×C₃₁	—	4	8	no	—
186	#41×C₃₁	—	4	16	no	—
187	#41×C₃₁	—	4	8	no	—
188	#41×C₃₁	—	4	4	no	—
189	#41×C₃₁	—	8	4	no	—
190	C₂×Q₈×C₃₁	—	2	1	no	—
191	C₂×Q₈×C₃₁	—	2	4	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	1	no	—
194	C₂×Q₈×C₃₁	—	2	2	no	—
195	C₂×Q₈×C₃₁	—	4	8	no	—
196	C₂×Q₈×C₃₁	—	4	8	no	—
197	C₂×Q₈×C₃₁	—	4	4	no	—
198	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	2	no	—
202	C₂×D₄×C₃₁	—	2	4	no	—
203	C₂×D₄×C₃₁	—	2	4	no	—
204	C₂×D₄×C₃₁	—	2	1	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	1	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	4	4	no	—
212	C₂×D₄×C₃₁	—	4	4	no	—
213	C₂×D₄×C₃₁	—	8	2	no	—
214	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
217	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	4	no	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
230	SD₁₆×C₃₁	—	4	4	no	—
231	D₈×C₃₁	—	4	8	no	—
232	M₁₆×C₃₁	—	4	4	no	—
233	C₂×C₈×C₃₁	—	4	2	no	—
234	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
235	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₃₁	—	2	2	no	—
238	C₄⋊C₄×C₃₁	—	2	1	no	—
239	C₄⋊C₄×C₃₁	—	2	4	no	—
240	C₄⋊C₄×C₃₁	—	2	2	no	—
241	C₄⋊C₄×C₃₁	—	2	4	no	—
242	C₄⋊C₄×C₃₁	—	2	2	no	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	1	no	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
253	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²⋊C₄×C₃₁	—	2	2	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
266	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₄²×C₃₁	—	2	2	no	—
268	C₄²×C₃₁	C₂×D₄	1	2	yes	—
269	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₃₁	C₂×D₄	1	2	yes	—
271	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₄²×C₃₁	C₂⁴	1	2	yes	—
275	#62541	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	4	no	—
278	C₂³×C₃₁	—	4	4	no	—
279	C₂³×C₃₁	—	8	2	no	—
280	C₂³×C₃₁	—	8	2	no	—
281	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
282	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₃₁	—	2	2	no	—
284	Q₈×C₃₁	—	2	4	no	—
285	Q₈×C₃₁	—	4	8	no	—
286	Q₈×C₃₁	—	4	2	no	—
287	Q₈×C₃₁	—	4	4	no	—
288	Q₈×C₃₁	—	4	4	no	—
289	Q₈×C₃₁	—	4	2	no	—
290	D₄×C₃₁	—	2	4	no	—
291	D₄×C₃₁	—	2	2	no	—
292	D₄×C₃₁	—	2	4	no	—
293	D₄×C₃₁	—	2	8	no	—
294	D₄×C₃₁	—	4	8	no	—
295	D₄×C₃₁	—	4	4	no	—
296	D₄×C₃₁	—	4	4	no	—
297	D₄×C₃₁	—	4	4	no	—
298	D₄×C₃₁	—	4	2	no	—
299	D₄×C₃₁	—	4	2	no	—
300	D₄×C₃₁	—	4	4	no	—
301	D₄×C₃₁	—	8	2	no	—
302	D₄×C₃₁	—	8	2	no	—
303	D₄×C₃₁	—	8	4	no	—
304	D₄×C₃₁	—	8	4	no	—
305	C₂×C₄×C₃₁	—	2	4	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	4	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	4	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	4	8	no	—
315	C₂×C₄×C₃₁	—	4	8	no	—
316	C₂×C₄×C₃₁	—	4	4	no	—
317	C₂×C₄×C₃₁	—	4	4	no	—
318	C₂×C₄×C₃₁	—	8	4	no	—
319	C₂×C₄×C₃₁	—	8	4	no	—
320	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
321	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
330	C₈×C₃₁	—	2	2	no	—
331	C₈×C₃₁	—	2	2	no	—
332	C₈×C₃₁	—	2	4	no	—
333	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
335	#3373	C₂×C₃₁	1	4	yes	complemented
336	#3332	C₂×C₃₁	1	4	yes	complemented
337	#3306	C₂×C₃₁	1	8	yes	complemented
338	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#3227	C₂×C₃₁	1	2	yes	complemented
340	#3207	C₂×C₃₁	1	2	yes	complemented
341	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3184	C₂×C₃₁	1	2	yes	complemented
343	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3141	C₂×C₃₁	1	2	yes	complemented
345	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#2965	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂²×C₃₁	—	2	1	no	—
348	C₂²×C₃₁	—	2	1	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	2	no	—
351	C₂²×C₃₁	—	2	2	no	—
352	C₂²×C₃₁	—	4	4	no	—
353	C₂²×C₃₁	—	4	2	no	—
354	C₂²×C₃₁	—	4	2	no	—
355	C₂²×C₃₁	—	4	4	no	—
356	C₂²×C₃₁	—	4	4	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	—	16	4	no	—
359	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
360	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₃₁	—	2	2	no	—
362	C₄×C₃₁	—	2	1	no	—
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	2	2	no	—
365	C₄×C₃₁	—	2	1	no	—
366	C₄×C₃₁	—	4	2	no	—
367	C₄×C₃₁	—	4	4	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
371	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
372	C₄×C₃₁	#577	1	2	yes	—
373	C₄×C₃₁	#585	1	2	yes	—
374	C₂×2₋¹⁺⁴	—	2	1	no	—
375	#559	—	2	1	no	—
376	#559	C₂²×C₃₁	1	2	yes	—
377	#550	—	2	1	no	—
378	#550	C₂²×C₃₁	1	2	yes	—
379	D₄×Q₈	—	2	1	no	—
380	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
381	#547	—	2	2	no	—
382	#547	—	2	1	no	—
383	#547	C₂²×C₃₁	1	4	yes	—
384	#547	C₂²×C₃₁	1	2	yes	complemented
385	#546	—	2	2	no	—
386	#546	C₂²×C₃₁	1	4	yes	—
387	#540	—	2	2	no	—
388	#536	—	2	1	no	—
389	#536	—	2	2	no	—
390	#535	—	2	1	no	—
391	#533	C₂²×C₃₁	1	1	yes	characteristic
392	#532	C₂²×C₃₁	1	2	yes	—
393	#532	C₂²×C₃₁	1	1	yes	characteristic
394	#532	C₂²×C₃₁	1	2	yes	—
395	#532	C₂²×C₃₁	1	2	yes	complemented
396	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
397	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
398	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
399	#518	—	2	1	no	—
400	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
401	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	#498	C₂²×C₃₁	1	2	yes	complemented
403	#493	C₂²×C₃₁	1	2	yes	—
404	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	#489	C₂²×C₃₁	1	8	yes	complemented
406	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	#487	C₂²×C₃₁	1	2	yes	complemented
408	#486	C₂²×C₃₁	1	4	yes	—
409	#486	C₂²×C₃₁	1	2	yes	—
410	#486	C₂²×C₃₁	1	2	yes	—
411	#486	C₂²×C₃₁	1	2	yes	—
412	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	#483	C₂²×C₃₁	1	4	yes	—
414	#481	C₂²×C₃₁	1	8	yes	complemented
415	#476	C₂²×C₃₁	1	8	yes	complemented
416	#475	C₂²×C₃₁	1	4	yes	complemented
417	#469	C₂²×C₃₁	1	8	yes	complemented
418	#465	C₂²×C₃₁	1	4	yes	—
419	#463	C₂²×C₃₁	1	8	yes	complemented
420	#459	C₂²×C₃₁	1	4	yes	—
421	#449	C₂²×C₃₁	1	8	yes	complemented
422	#447	C₂²×C₃₁	1	4	yes	—
423	#446	C₂²×C₃₁	1	2	yes	complemented
424	#442	C₂²×C₃₁	1	8	yes	complemented
425	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
426	#436	C₂²×C₃₁	1	2	yes	complemented
427	#435	C₂²×C₃₁	1	4	yes	—
428	#431	C₂²×C₃₁	1	1	yes	characteristic
429	#431	C₂²×C₃₁	1	2	yes	complemented
430	#417	C₂²×C₃₁	1	8	yes	complemented
431	C₂×#102	C₂²×C₃₁	1	4	yes	—
432	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
433	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×C₃₁	—	2	2	no	—
435	C₂×C₃₁	—	4	2	no	—
436	C₂×C₃₁	—	8	2	no	—
437	C₂×C₃₁	—	8	4	no	—
438	C₂×C₃₁	#3500	1	1	yes	characteristic
439	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
441	2₋¹⁺⁴	—	4	8	no	—
442	C₂×#41	—	2	4	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
448	C₂×#41	C₂³×C₃₁	1	4	yes	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×Q₈	—	2	2	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
455	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
456	C₂×D₈	C₂³×C₃₁	1	8	yes	—
457	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
458	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
468	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
469	#127	—	2	2	no	—
470	#127	—	2	1	no	—
471	#127	—	2	1	no	—
472	#127	C₂³×C₃₁	1	2	yes	—
473	#127	C₂³×C₃₁	1	2	yes	—
474	#127	C₂³×C₃₁	1	1	yes	characteristic
475	#125	—	2	1	no	—
476	#124	—	2	2	no	—
477	#124	—	2	1	no	—
478	#124	—	2	2	no	—
479	#124	—	2	2	no	—
480	#124	C₂³×C₃₁	1	4	yes	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	1	no	—
496	#121	—	2	2	no	—
497	#121	—	2	4	no	—
498	#121	—	2	4	no	—
499	#121	C₂³×C₃₁	1	4	yes	—
500	#121	C₂³×C₃₁	1	2	yes	—
501	#121	C₂³×C₃₁	1	4	yes	—
502	#120	—	2	4	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
505	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
506	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	D₄×C₃₁	1	2	yes	—
515	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
516	C₄×D₄	C₂³×C₃₁	1	4	yes	—
517	C₄×D₄	C₂³×C₃₁	1	2	yes	—
518	C₄×D₄	C₂³×C₃₁	1	4	yes	—
519	C₄×D₄	C₂³×C₃₁	1	2	yes	—
520	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
521	#117	—	2	1	no	—
522	#117	D₄×C₃₁	1	1	yes	characteristic
523	#117	D₄×C₃₁	1	2	yes	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
528	C₂×C₂²⋊C₄	—	2	4	no	—
529	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
531	#106	C₂³×C₃₁	1	4	yes	—
532	#106	C₂³×C₃₁	1	8	yes	—
533	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
534	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
535	#103	C₂³×C₃₁	1	4	yes	—
536	#103	C₂³×C₃₁	1	8	yes	—
537	#102	C₂³×C₃₁	1	8	yes	—
538	#102	C₂³×C₃₁	1	8	yes	—
539	#102	C₂³×C₃₁	1	8	yes	—
540	#102	C₂³×C₃₁	1	4	yes	—
541	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
542	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
543	#97	C₂³×C₃₁	1	4	yes	—
544	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
546	C₄×C₈	C₂³×C₃₁	1	2	yes	—
547	C₄×C₈	C₂³×C₃₁	1	2	yes	—
548	C₃₁	#62541	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁴	—	2	2	no	—
550	#41	—	2	4	no	—
551	#41	—	4	8	no	—
552	#41	—	4	8	no	—
553	#41	—	4	16	no	—
554	#41	—	4	8	no	—
555	#41	—	4	4	no	—
556	#41	—	8	4	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	4	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	4	8	no	—
563	C₂×Q₈	—	4	8	no	—
564	C₂×Q₈	—	4	4	no	—
565	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
566	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	8	2	no	—
581	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
582	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
583	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
584	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
592	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
597	SD₁₆	—	4	4	no	—
598	D₈	—	4	8	no	—
599	M₁₆	—	4	4	no	—
600	C₂×C₈	—	4	2	no	—
601	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
602	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
603	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
619	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
620	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₄²	—	2	2	no	—
635	C₄²	C₂×D₄×C₃₁	1	2	yes	—
636	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₃₁	1	2	yes	—
638	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
639	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₄²	C₂⁴×C₃₁	1	2	yes	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	8	2	no	—
646	C₂³	—	8	2	no	—
647	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
648	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
649	Q₈	—	2	2	no	—
650	Q₈	—	2	4	no	—
651	Q₈	—	4	8	no	—
652	Q₈	—	4	2	no	—
653	Q₈	—	4	4	no	—
654	Q₈	—	4	4	no	—
655	Q₈	—	4	2	no	—
656	D₄	—	2	4	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	4	no	—
659	D₄	—	2	8	no	—
660	D₄	—	4	8	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	4	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	8	2	no	—
668	D₄	—	8	2	no	—
669	D₄	—	8	4	no	—
670	D₄	—	8	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
695	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
696	C₈	—	2	2	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	4	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	16	4	no	—
711	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
712	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
713	C₄	—	2	2	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	1	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	4	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
723	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
724	C₄	C₃₁×#577	1	2	yes	—
725	C₄	C₃₁×#585	1	2	yes	—
726	C₂	—	2	2	no	—
727	C₂	—	4	2	no	—
728	C₂	—	8	4	no	—
729	C₂	—	8	2	no	—
730	C₂	C₃₁×#3500	1	1	yes	characteristic
731	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
732	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3499	C₂	semidirect
3. C₃₁×#3373	C₂	semidirect
4. C₃₁×#3332	C₂	semidirect
5. C₃₁×#3306	C₂	semidirect
6. C₃₁×#3229	C₂	semidirect
7. C₃₁×#3227	C₂	semidirect
8. C₃₁×#3207	C₂	semidirect
9. C₃₁×#3205	C₂	semidirect
10. C₃₁×#3184	C₂	semidirect
11. C₃₁×#3167	C₂	semidirect
12. C₃₁×#3141	C₂	semidirect
13. C₂×C₃₁×#486	C₂	semidirect
14. C₃₁×#2965	C₂	semidirect
21. D₄×Q₈×C₃₁	C₂²	semidirect
25. C₃₁×#547	C₂²	semidirect
36. C₃₁×#532	C₂²	semidirect
38. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₃₁×#498	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
45. C₃₁×#492	C₂²	semidirect
46. C₃₁×#489	C₂²	semidirect
47. C₃₁×#487	C₂²	semidirect
48. C₃₁×#487	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#476	C₂²	semidirect
57. C₃₁×#475	C₂²	semidirect
58. C₃₁×#469	C₂²	semidirect
60. C₃₁×#463	C₂²	semidirect
62. C₃₁×#449	C₂²	semidirect
64. C₃₁×#446	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₄×SD₁₆×C₃₁	C₂²	semidirect
67. C₃₁×#436	C₂²	semidirect
70. C₃₁×#431	C₂²	semidirect
71. C₃₁×#417	C₂²	semidirect
73. C₄×M₁₆×C₃₁	C₂²	semidirect
275. #62541	C₃₁	direct (N × H)
333. #3508	C₂×C₃₁	semidirect
334. #3499	C₂×C₃₁	semidirect
335. #3373	C₂×C₃₁	semidirect
336. #3332	C₂×C₃₁	semidirect
337. #3306	C₂×C₃₁	semidirect
338. #3229	C₂×C₃₁	semidirect
339. #3227	C₂×C₃₁	semidirect
340. #3207	C₂×C₃₁	semidirect
341. #3205	C₂×C₃₁	semidirect
342. #3184	C₂×C₃₁	semidirect
343. #3167	C₂×C₃₁	semidirect
344. #3141	C₂×C₃₁	semidirect
345. C₂×#486	C₂×C₃₁	semidirect
346. #2965	C₂×C₃₁	semidirect
380. D₄×Q₈	C₂²×C₃₁	semidirect
384. #547	C₂²×C₃₁	semidirect
395. #532	C₂²×C₃₁	semidirect
397. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
401. #498	C₂²×C₃₁	semidirect
402. #498	C₂²×C₃₁	semidirect
404. #492	C₂²×C₃₁	semidirect
405. #489	C₂²×C₃₁	semidirect
406. #487	C₂²×C₃₁	semidirect
407. #487	C₂²×C₃₁	semidirect
412. #486	C₂²×C₃₁	semidirect
414. #481	C₂²×C₃₁	semidirect
415. #476	C₂²×C₃₁	semidirect
416. #475	C₂²×C₃₁	semidirect
417. #469	C₂²×C₃₁	semidirect
419. #463	C₂²×C₃₁	semidirect
421. #449	C₂²×C₃₁	semidirect
423. #446	C₂²×C₃₁	semidirect
424. #442	C₂²×C₃₁	semidirect
425. C₄×SD₁₆	C₂²×C₃₁	semidirect
426. #436	C₂²×C₃₁	semidirect
429. #431	C₂²×C₃₁	semidirect
430. #417	C₂²×C₃₁	semidirect
432. C₄×M₁₆	C₂²×C₃₁	semidirect
548. C₃₁	#62541	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3508	2
C₃₁×#3499	2
C₃₁×#3373	2
C₃₁×#3332	2
C₃₁×#3306	2
C₃₁×#3229	2
C₃₁×#3227	2
C₃₁×#3207	2
C₃₁×#3205	2
C₃₁×#3184	2
C₃₁×#3167	2
C₃₁×#3141	2
C₂×C₃₁×#486	2
C₃₁×#2965	2
#62541	31

Subgroups — C31×#62541 #21519300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62541 #21519300